These images consistently confirm that the axial plane LR muscle path, even in central gaze, is neither a straight path nor the shortest path from origin to scleral insertion. Instead, the LR path is inflected toward the orbital wall a distance averaging some 11 to 14 mm posterior to globe center. This lateral inflection, seen in axial MRI, is posterior to the transverse inflection in LR path produced by the LR pulley, which lies 10 mm posterior to the globe center in central gaze in the coordinate system used here.
7 The normal LR belly consistently appears separated from the anterior periorbita by a buffer of fat that has been presumed to confine the EOM. The present data, however, are interpreted differently from both these foregoing presumptions. Although the internal rigidity of EOMs has not been measured, whatever rigidity normally exists would also oppose lateral LR path inflection.
In contrast to the robust cross-sections of normal LR muscles, paralyzed LR muscles develop no active tension and exhibit striking denervation atrophy.
25 The paralyzed LR is not only flaccid, it also must be presumed to have less internal rigidity than the normal LR because it is smaller than normal. In this study, MRI consistently demonstrated the paralyzed LR to be thin and pressed against the periorbita in its posterior course
(Figs. 1 2 3) . This implies that the posterior orbital fat does not confine and prohibit the LR from contact with the periorbital; rather, it suggests that the orbital fat may flow in to fill the void between the LR and the periorbita that is produced by a different mechanical constraint. In the present study, MRI showed that the anterior portion of the paralyzed LR, probably also the thinnest because of normal transition from muscle fibers to terminal tendon, was sharply inflected so that it was not directly apposed to the periorbita beginning approximately 13 mm posterior to the globe center. Rather than a diffuse effect of homogeneous orbital fat, the sharper inflection of the paralyzed LR must be caused by inhomogeneity, the focal effect of other connective tissues. It is proposed that these connective tissues are in actuality the LR pulley sleeve.
The path behavior of the innervated but highly relaxed LR in comitant ET is similar in some respects to that of the paralyzed LR. As illustrated in
Figure 2 , for a large angle of ET similar to LR palsy, the highly relaxed but nonparalytic LR also exhibits a substantial lateral path inflection
(Fig. 2B) . Although neurogenic atrophy of the paralyzed LR may make this inflection more conspicuous, quantitative properties of the inflection are similar to the situation of extreme LR relaxation without atrophy. One difference is that the anteroposterior location of the inflection of the paralyzed LR shifts more with duction than does the normal LR or the LR in concomitant ET. This may reflect the presumably lower elastic tension in the paralyzed LR than in a relaxed but innervated LR.
Biomechanical data are lacking for most orbital tissues, including EOMs. Direct mechanical measurements of many mechanical properties are not likely to be possible in human tissues. Although the distributions of connective tissues in the pulley system have been measured,
3 these data at best provide only relative, not absolute, indicators of tissue stiffness. The current observations concerning LR path inflection provide additional relative measures.
Schutte et al.
24 have used a finite element model (FEM) to support their proposal that orbital “fat,” rather than the connective tissue pulley system, stabilizes EOM paths. This FEM assumed that all materials except EOMs were homogeneous and isotropic and that, in addition to the globe and EOMs, the orbit contained only an incompressible material denoted as fat. For computational convenience, the fat was represented by a variably coarse mesh of tetrahedral volume elements. Although the optic nerve and connective tissues considered by others to be the pulley system
3 4 9 10 11 12 16 17 18 19 20 21 22 29 were lumped into the isotropic mechanical properties of fat, the fat was considered to have an abrupt discontinuity at the border of a hypothetical muscle cone, defined by lines connecting the centers of the rectus EOMs. Although histologic examination provides no anatomic justification for the existence of a muscle cone or any reason to suspect differences in fat lying inside or outside it,
3 Schutte et al.
24 assumed a Young’s modulus (ratio of stress to strain in the linear region) of 300 Pa for the intraconal fat, abruptly increasing to 1000 Pa for the extraconal fat. A Young’s modulus of 300 Pa resembles the behavior of a 10% solution of gelatin in water,
30 so the FEM assumes that intraconal fat is nearly liquid but that the EOMs themselves are externally encased in extraconal fat that is more than threefold more resistant to shear. The Schutte et al.
24 FEM also assumed a Young’s modulus of 40 kPa for human EOMs. In contrast, unpublished data from my laboratory indicate a Young’s modulus of approximately 700 kPa for bovine EOMs (Yoo L, unpublished observations, 2008). It is thus evident that the Schutte et al.
24 FEM actually makes a strong assumption about a major discontinuity in the Young’s modulus of the orbital fat at the intraconal-extraconal junction while also assuming a low Young’s modulus for EOMs.
The FEM of Schutte et al.
24 was limited to ocular ductions of less than 15° due to the use of a thin, low-elasticity interface to approximate sliding of EOM tendons over the sclera that, by computational necessity, prohibited much actual sliding motion. Larger rotations caused the tetrahedron volume elements to turn inside out,
24 a situation so grossly unrealistic that FEM behavior for modestly smaller ductions would also be questionable. Sliding between the globe and the posterior Tenon fascia was neglected altogether in the Schutte et al.
24 FEM on the assumption that the retrobulbar fat is in direct contact with the globe and has negligible elasticity. These assumptions, which limit or ignore sliding, are neither anatomically nor mechanically realistic but are likely to have resulted in the EOM path stability that Schutte et al.
24 claim as the important emergent feature of the FEM. Given that the simulated EOM tendons are artificially prohibited from sliding over the globe in the FEM, their paths are “stuck” to the underlying surface of the globe surface whenever the tendons make globe contact. It is thus true by assumption that the simulated EOM tendons must bend to move with globe rotation. Where they are not in contact with the globe, more posterior portions of the highly elastic simulated EOM bellies are, not surprisingly, constrained by the assumption of relatively high stiffness of the extraconal fat located between them. This behavior arises from unrealistic anatomic assumptions in the FEM and should not be interpreted to negate the influence of actual anatomic structures such as the orbital connective tissues. In reality, the anatomic ocular globe is suspended by the thick concave surface of posterior Tenon fascia, formed of particularly dense collagen and elastin reinforced by smooth muscle.
4 Pulleys, composed of dense collagen and elastin encirclements of each of the four rectus EOMs where the EOMs penetrate the posterior Tenon fascia, are suspended from nasal and temporal anchors on the orbital walls.
3
It is proposed here that efforts to understand the mechanical behavior of the EOMs and orbital tissues should remain grounded in anatomic realism. Although this mechanical behavior is so complex that detailed models of it must be computationally intensive, computational convenience should not trump anatomic accuracy. The present finding of a lateral inflection in path of the slack LR argues against the assumptions that the orbital tissues consist of isotropic and homogeneous fat. Alternatively, it is suggested that the known structure of lumped orbital connective tissue structures—the pulleys and their suspensions—can account for the present finding of lateral inflection in the path of the slack LR.
It is also proposed that stiffness of the posterior portion of the LR pulley sleeve is low enough that normal LR tension deflects the posterior mouth of the sleeve medially
(Fig. 7A) . When the LR is paralyzed and chronically atrophic, or when it is maximally relaxed in concomitant esotropia, LR tension is significantly lower than normal tension in the LR pulley suspension, which then pulls the LR pulley adjacent the orbital wall, displacing the mobile fat
(Figs. 7B 7C) . Even so, the passive elastic tension in the slack LR is sufficient to deflect nasally what can be inferred to be the thin and elastic tissue at the posterior apex of the LR pulley sleeve
(Fig. 7B) . However, when the medial rectus relaxes to permit the eye to abduct slightly into the paralyzed LR’s field of action, passive LR tension decreases because LR path length is reduced
(Fig. 7C) . The decrease in passive elastic tension in the paralyzed LR allows the thin posterior apex of the LR pulley sleeve to straighten
(Fig. 7C) , shifting posteriorly the inflection point in LR path, as observed in the present data
(Fig. 6B) . The posterior shift in LR inflection permits the inference that the stiffness of the posterior apex of the LR pulley sleeve must be greater than the transverse component of the passive elastic tension of a paralyzed LR when the LR is subjected to further relaxation.
Quantitative modeling of biological materials remains a complex and evolving field, subject to continuing development of even the most fundamental theoretical approaches.
31 Even the types of tissue properties mechanically relevant to modeling remain under fundamental debate, and these are markedly nonlinear with respect to static and dynamic factors. In such a setting, it is prudent support functional conclusions with a wide variety of quantitative and qualitative observations. The present observations concerning the path of the paralyzed or maximally relaxed LR can suggest only bounds and relative values of stiffness of pulley tissues in comparison with EOM tensions. Of course, there is a need for more and better measurements of the biomechanical properties of the EOMs and orbital connective tissues, including fat. While lumping orbital fat with connective tissues has suggested the order of magnitude of average elasticities and viscosities,
30 accurate modeling will require parameterization of specific connective tissue components, particularly in the pulleys and their suspensions. Models based on observed parameters will have to conform to the behavior observed here for the paralyzed and relaxed LR.